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NASA NTRS1994

Parallel, adaptive finite element methods for conservation laws

We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.

Biswas, Rupak↗

NASA NTRS1994

Design and implementation of a parallel unstructured Euler solver using software primitives

This paper is concerned with the implementation of a three-dimensional unstructured-grid Euler solver on massively parallel distributed-memory computer architectures. The goal is to minimize solution time by achieving high computational rates with a numerically efficient algorithm. An unstructured multigrid algorithm with an edge-based data structure has been adopted, and a number of optimizations have been devised and implemented to accelerate the parallel computational rates. The implementation is carried out by creating a set of software tools, which provide an interface between the parallelization issues and the sequential code, while providing a basis for future automatic run-time compilation support. Large practical unstructured grid problems are solved on the Intel iPSC/860 hypercube and Intel Touchstone Delta machine. The quantitative effects of the various optimizations are demonstrated, and we show that the combined effect of these optimizations leads to roughly a factor of 3 performance improvement. The overall solution efficiency is compared with that obtained on the Cray Y-MP vector supercomputer.

Das, R.↗

NASA NTRS1995

Communication overhead on the Intel Paragon, IBM SP2 and Meiko CS-2

Interprocessor communication overhead is a crucial measure of the power of parallel computing systems-its impact can severely limit the performance of parallel programs. This report presents measurements of communication overhead on three contemporary commercial multicomputer systems: the Intel Paragon, the IBM SP2 and the Meiko CS-2. In each case the time to communicate between processors is presented as a function of message length. The time for global synchronization and memory access is discussed. The performance of these machines in emulating hypercubes and executing random pairwise exchanges is also investigated. It is shown that the interprocessor communication time depends heavily on the specific communication pattern required. These observations contradict the commonly held belief that communication overhead on contemporary machines is independent of the placement of tasks on processors. The information presented in this report permits the evaluation of the efficiency of parallel algorithm implementations against standard baselines.

Bokhari, Shahid H.↗

NASA NTRS1994

High dimensional feature reduction via projection pursuit

The recent development of more sophisticated remote sensing systems enables the measurement of radiation in many more spectral intervals than previously possible. An example of that technology is the AVIRIS system, which collects image data in 220 bands. As a result of this, new algorithms must be developed in order to analyze the more complex data effectively. Data in a high dimensional space presents a substantial challenge, since intuitive concepts valid in a 2-3 dimensional space to not necessarily apply in higher dimensional spaces. For example, high dimensional space is mostly empty. This results from the concentration of data in the corners of hypercubes. Other examples may be cited. Such observations suggest the need to project data to a subspace of a much lower dimension on a problem specific basis in such a manner that information is not lost. Projection Pursuit is a technique that will accomplish such a goal. Since it processes data in lower dimensions, it should avoid many of the difficulties of high dimensional spaces. In this paper, we begin the investigation of some of the properties of Projection Pursuit for this purpose.

Jimenez, Luis↗

NASA NTRS1996

Parallelization of Finite Element Analysis Codes Using Heterogeneous Distributed Computing

Performance gains in computer design are quickly consumed as users seek to analyze larger problems to a higher degree of accuracy. Innovative computational methods, such as parallel and distributed computing, seek to multiply the power of existing hardware technology to satisfy the computational demands of large applications. In the early stages of this project, experiments were performed using two large, coarse-grained applications, CSTEM and METCAN. These applications were parallelized on an Intel iPSC/860 hypercube. It was found that the overall speedup was very low, due to large, inherently sequential code segments present in the applications. The overall execution time T(sub par), of the application is dependent on these sequential segments. If these segments make up a significant fraction of the overall code, the application will have a poor speedup measure.

Ozguner, Fusun↗

NASA NTRS1998

The Wavelet Element Method: Realization and Additional Features in 2D and 3D - Part 2

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interelement boundaries, a globally continuous biorthogonal wavelet basis on the general domain is obtained. This construction does not uniquely define the basis functions but rather leaves some freedom for fulfilling additional features. In this paper we detail the general construction principle of the WEM to the 1D, 2D and 3D cases. We address additional features such as symmetry, vanishing moments and minimal support of the wavelet functions in each particular dimension. The construction is illustrated by using biorthogonal spline wavelets on the interval.

Canuto, Claudio↗

NASA NTRS1998

A Monte Carlo Uncertainty Analysis of Ozone Trend Predictions in a Two Dimensional Model

We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two-dimensional (2D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas-phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin Hypercube Sampling. The standard deviation (a) of the Monte Carlo ensemble of total 03 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1 (sigma), model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total 03 trends differ by more than 1(sigma) but less than 2(sigma), which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak-to-peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation problems and provide a measure of model performance which can be used in attempts to improve such models.

Considine, D. B.↗

NASA NTRS2000

Uncertainty Analysis of Decomposing Polyurethane Foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. Related polyurethane binders such as Estane are used in many energetic materials of interest to the JANNAF community. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state decomposition front velocity calculated as the derivative of the decomposition front location versus time. An analytical mean value sensitivity/uncertainty (MV) analysis was used to determine the standard deviation by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation was essentially determined from a second derivative that was extremely sensitive to numerical noise. To minimize the numerical noise, 50-micrometer element dimensions and approximately 1-msec time steps were required to obtain stable uncertainty results. As an alternative method to determine the uncertainty and sensitivity in the decomposition front velocity, surrogate response surfaces were generated for use with a constrained Latin Hypercube Sampling (LHS) technique. Two surrogate response surfaces were investigated: 1) a linear surrogate response surface (LIN) and 2) a quadratic response surface (QUAD). The LHS techniques do not require derivatives of the response variable and are subsequently relatively insensitive to numerical noise. To compare the LIN and QUAD methods to the MV method, a direct LHS analysis (DLHS) was performed using the full grid and timestep resolved finite element model. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.

Hobbs, Michael L.↗

NASA NTRS1994

Automated Instrumentation and Monitoring of Data Movement for Parallel Programs

Writing efficient parallel programs is complicated by the need to select the right data structure alignments and distributions, which determine the nature and volume of inter-processor communications. A large number of performance tools for parallel programs have been developed recently to expose these inter-processor communications. However, none of them support performance views or provide statistics in terms of inter-processor data structure interactions. A performance tool that tracks the interaction between individual data structures and the context of these interactions is essential for understanding the performance of both explicit message passing programs and data-parallel languages such as HPF. In this paper we discuss the use of compiler front end tools for automatically tracking data structure movements in message passing programs, and low-overhead monitoring and postprocessing of such codes. We demonstrate that robust instrumentation and low overhead monitoring of inter-processor data structure movements is possible, with the use of a number of NAS benchmark codes, run on the i860 hypercube. We also show that the data so collected can be used effectively by post processing tools that expose performance bottlenecks using graphical displays and performance statistics.

Sarukkai, Sekhar↗

NASA NTRS1994

Toward Automatic Scalability Analysis of Message Passing Programs: A Case Study

Scalability analysis forms an important component of any performance debugging cycle, for massively parallel machines. However, tools that help in performing such analysis for parallel programs are non-existent. The primary reason for lack of such tools is the complexity involved in capturing program dynamics such as communication-computation overlap, communication latencies and memory hierarchy reference patterns. In this paper, we highlight some simple techniques that can be used to study scalability of explicit message-passing parallel programs that consider the above issues. We start from the high level source code and use a methodology for deducing communication characteristics and its impact on the total execution time of the program. The approach is validated with the help of a pipelined method for solving scalar tri-diagonal systems, using both simulations and symbolic cost models on the Intel hypercube.

Sarukkai, Sekhar R.↗

NASA NTRS2002

Probabilistic Analysis and Density Parameter Estimation Within Nessus

This NASA educational grant has the goal of promoting probabilistic analysis methods to undergraduate and graduate UTSA engineering students. Two undergraduate-level and one graduate-level course were offered at UTSA providing a large number of students exposure to and experience in probabilistic techniques. The grant provided two research engineers from Southwest Research Institute the opportunity to teach these courses at UTSA, thereby exposing a large number of students to practical applications of probabilistic methods and state-of-the-art computational methods. In classroom activities, students were introduced to the NESSUS computer program, which embodies many algorithms in probabilistic simulation and reliability analysis. Because the NESSUS program is used at UTSA in both student research projects and selected courses, a student version of a NESSUS manual has been revised and improved, with additional example problems being added to expand the scope of the example application problems. This report documents two research accomplishments in the integration of a new sampling algorithm into NESSUS and in the testing of the new algorithm. The new Latin Hypercube Sampling (LHS) subroutines use the latest NESSUS input file format and specific files for writing output. The LHS subroutines are called out early in the program so that no unnecessary calculations are performed. Proper correlation between sets of multidimensional coordinates can be obtained by using NESSUS' LHS capabilities. Finally, two types of correlation are written to the appropriate output file. The program enhancement was tested by repeatedly estimating the mean, standard deviation, and 99th percentile of four different responses using Monte Carlo (MC) and LHS. These test cases, put forth by the Society of Automotive Engineers, are used to compare probabilistic methods. For all test cases, it is shown that LHS has a lower estimation error than MC when used to estimate the mean, standard deviation, and 99th percentile of the four responses at the 50 percent confidence level and using the same number of response evaluations for each method. In addition, LHS requires fewer calculations than MC in order to be 99.7 percent confident that a single mean, standard deviation, or 99th percentile estimate will be within at most 3 percent of the true value of the each parameter. Again, this is shown for all of the test cases studied. For that reason it can be said that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ; furthermore, the newest LHS module is a valuable new enhancement of the program.

Godines, Cody R.↗

NASA NTRS2003

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗

NASA NTRS1989

Multinode reconfigurable pipeline computer

A multinode parallel-processing computer is made up of a plurality of innerconnected, large capacity nodes each including a reconfigurable pipeline of functional units such as Integer Arithmetic Logic Processors, Floating Point Arithmetic Processors, Special Purpose Processors, etc. The reconfigurable pipeline of each node is connected to a multiplane memory by a Memory-ALU switch NETwork (MASNET). The reconfigurable pipeline includes three (3) basic substructures formed from functional units which have been found to be sufficient to perform the bulk of all calculations. The MASNET controls the flow of signals from the memory planes to the reconfigurable pipeline and vice versa. the nodes are connectable together by an internode data router (hyperspace router) so as to form a hypercube configuration. The capability of the nodes to conditionally configure the pipeline at each tick of the clock, without requiring a pipeline flush, permits many powerful algorithms to be implemented directly.

Nosenchuck, Daniel M.↗

NASA NTRS1986

NASA Tech Briefs, November/December 1986, Special Edition

Topics: Computing: The View from NASA Headquarters; Earth Resources Laboratory Applications Software: Versatile Tool for Data Analysis; The Hypercube: Cost-Effective Supercomputing; Artificial Intelligence: Rendezvous with NASA; NASA's Ada Connection; COSMIC: NASA's Software Treasurehouse; Golden Oldies: Tried and True NASA Software; Computer Technical Briefs; NASA TU Services; Digital Fly-by-Wire.

Source record↗

NASA NTRS2013

Using Response Surface Methods to Correlate the Modal Test of an Inflatable Test Article

This paper presents a practical application of response surface methods (RSM) to correlate a finite element model of a structural modal test. The test article is a quasi‐cylindrical inflatable structure which primarily consists of a fabric weave, with an internal bladder and metallic bulkheads on either end. To mitigate model size, the fabric weave was simplified by representing it with shell elements. The task at hand is to represent the material behavior of the weave. The success of the model correlation is measured by comparing the four major modal frequencies of the analysis model to the four major modal frequencies of the test article. Given that only individual strap material properties were provided and material properties of the overall weave were not available, defining the material properties of the finite element model became very complex. First it was necessary to determine which material properties (modulus of elasticity in the hoop and longitudinal directions, shear modulus, Poisson's ratio, etc.) affected the modal frequencies. Then a Latin Hypercube of the parameter space was created to form an efficiently distributed finite case set. Each case was then analyzed with the results input into RSM. In the resulting response surface it was possible to see how each material parameter affected the modal frequencies of the analysis model. If the modal frequencies of the analysis model and its corresponding parameters match the test with acceptable accuracy, it can be said that the model correlation is successful.

Gupta, Anju↗

NASA NTRS2016

Microgravity-Driven Optic Nerve/Sheath Biomechanics Simulations

Visual Impairment and Intracranial Pressure (VIIP) syndrome is a concern for long-duration space flight. Current thinking suggests that the ocular changes observed in VIIP syndrome are related to cephalad fluid shifts resulting in altered fluid pressures [1]. In particular, we hypothesize that increased intracranial pressure (ICP) drives connective tissue remodeling of the posterior eye and optic nerve sheath (ONS). We describe here finite element (FE) modeling designed to understand how altered pressures, particularly altered ICP, affect the tissues of the posterior eye and optic nerve sheath (ONS) in VIIP. METHODS: Additional description of the modeling methodology is provided in the companion IWS abstract by Feola et al. In brief, a geometric model of the posterior eye and optic nerve, including the ONS, was created and the effects of fluid pressures on tissue deformations were simulated. We considered three ICP scenarios: an elevated ICP assumed to occur in chronic microgravity, and ICP in the upright and supine positions on earth. Within each scenario we used Latin hypercube sampling (LHS) to consider a range of ICPs, ONH tissue mechanical properties, intraocular pressures (IOPs) and mean arterial pressures (MAPs). The outcome measures were biomechanical strains in the lamina cribrosa, optic nerve and retina; here we focus on peak values of these strains, since elevated strain alters cell phenotype and induce tissue remodeling. In 3D, the strain field can be decomposed into three orthogonal components, denoted as first, second and third principal strains. RESULTS AND CONCLUSIONS: For baseline material properties, increasing ICP from 0 to 20 mmHg significantly changed strains within the posterior eye and ONS (Fig. 1), indicating that elevated ICP affects ocular tissue biomechanics. Notably, strains in the lamina cribrosa and retina became less extreme as ICP increased; however, within the optic nerve, the occurrence of such extreme strains greatly increased as ICP was elevated (Fig. 2). In particular, c. 48 of simulations in the elevated ICP condition showed peak strains in the optic nerve that exceeded the strains expected on earth. Such extreme strains are likely important, since they represent a larger signal for mechano-responsive resident cells [2]. The models predicted little to no anterior motion of the prelaminar neural tissue (optic nerve swelling, or papilledema, secondary to axoplasmic stasis), typically seen with elevated ICP. Specialized FE models to capture axoplasmic stasis would be required to study papilledema. These results suggest that the most notable effect of elevated ICP may occur via direct optic nerve loading, rather than through connective tissue deformation. These FE models can inform the design of future studies designed to bridge the gap between biomechanics and pathophysiological function in VIIP.

biomechanics↗

NASA NTRS2016

Probabilistic Modeling of Intracranial Pressure Effects on Optic Nerve Biomechanics

Altered intracranial pressure (ICP) is involved/implicated in several ocular conditions: papilledema, glaucoma and Visual Impairment and Intracranial Pressure (VIIP) syndrome. The biomechanical effects of altered ICP on optic nerve head (ONH) tissues in these conditions are uncertain but likely important. We have quantified ICP-induced deformations of ONH tissues, using finite element (FE) and probabilistic modeling (Latin Hypercube Simulations (LHS)) to consider a range of tissue properties and relevant pressures.

biomechanics↗

NASA NTRS2016

Influence of Population Variation of Physiological Parameters in Computational Models of Space Physiology

The earliest manifestations of Visual Impairment and Intracranial Pressure (VIIP) syndrome become evident after months of spaceflight and include a variety of ophthalmic changes, including posterior globe flattening and distension of the optic nerve sheath. Prevailing evidence links the occurrence of VIIP to the cephalic fluid shift induced by microgravity and the subsequent pressure changes around the optic nerve and eye. Deducing the etiology of VIIP is challenging due to the wide range of physiological parameters that may be influenced by spaceflight and are required to address a realistic spectrum of physiological responses. Here, we report on the application of an efficient approach to interrogating physiological parameter space through computational modeling. Specifically, we assess the influence of uncertainty in input parameters for two models of VIIP syndrome: a lumped-parameter model (LPM) of the cardiovascular and central nervous systems, and a finite-element model (FEM) of the posterior eye, optic nerve head (ONH) and optic nerve sheath. Methods: To investigate the parameter space in each model, we employed Latin hypercube sampling partial rank correlation coefficient (LHSPRCC) strategies. LHS techniques outperform Monte Carlo approaches by enforcing efficient sampling across the entire range of all parameters. The PRCC method estimates the sensitivity of model outputs to these parameters while adjusting for the linear effects of all other inputs. The LPM analysis addressed uncertainties in 42 physiological parameters, such as initial compartmental volume and nominal compartment percentage of total cardiac output in the supine state, while the FEM evaluated the effects on biomechanical strain from uncertainties in 23 material and pressure parameters for the ocular anatomy. Results and Conclusion: The LPM analysis identified several key factors including high sensitivity to the initial fluid distribution. The FEM study found that intraocular pressure and intracranial pressure had dominant impact on the peak strains in the ONH and retro-laminar optic nerve, respectively; optic nerve and lamina cribrosa stiffness were also important. This investigation illustrates the ability of LHSPRCC to identify the most influential physiological parameters, which must therefore be well-characterized to produce the most accurate numerical results.

biomechanics↗